Information-thermodynamic characterization of stochastic Boolean networks

Recent progress in experimental techniques has enabled us to quantitatively study stochastic and flexible behavior of biological systems. For example, gene regulatory networks perform stochastic information processing and their functionalities have been extensively studied. In gene regulatory networks, there are specific subgraphs called network motifs that occur at frequencies much higher than those found in randomized networks. Further understanding of the designing principle of such networks is highly desirable. In a different context, information thermodynamics has been developed as a theoretical framework that generalizes non-equilibrium thermodynamics to stochastically fluctuating systems with information. Here we systematically characterize gene regulatory networks on the basis of information thermodynamics. We model three-node gene regulatory patterns by a stochastic Boolean model, which receive one or two input signals that carry external information. For the case of a single input, we found that all the three-node patterns are classified into four types by using information-thermodynamic quantities such as dissipation and mutual information, and reveal to which type each network motif belongs. Next, we consider the case where there are two inputs, and evaluate the capacity of logical operation of the three-node patterns by using tripartite mutual information, and argue the reason why patterns with fewer edges are preferred in natural selection. This result might also explain the difference of the occurrence frequencies among different types of feedforward-loop network motifs.